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Briefly explain the meaning of each of the following terms. a. Null hypothesis b. Alternative hypothesis c. Critical point(s) d. Significance level e. Nonrejection region f. Rejection region g. Tails of a test h. Two types of errors

What are the four possible outcomes for a test of hypothesis? Show these outcomes by writing a table. Briefly describe the Type I and Type II errors.

Explain how the tails of a test depend on the sign in the alternative hypothesis. Describe the signs in the null and alternative hypotheses for a two-tailed, a left-tailed, and a right-tailed test, respectively.

Explain which of the following is a two-tailed test, a left-tailed test, or a right-tailed test. a. \(H_{0}=\mu=45, \quad H_{1}: \mu>45\) c. \(H_{0}: \mu \geq 75, \quad H_{1}: \mu<75\) b. \(H_{0}: \mu=23, \quad H_{1}: \mu \neq 23\) Show the rejection and nonrejection regions for each of these cases by drawing a sampling distribution curve for the sample mean, assuming that it is normally distributed.

Explain which of the following is a two-tailed test, a left-tailed test, or a right-tailed test. a. \(H_{0}: \mu=12, \quad H_{1}: \mu<12 \quad\) b. \(H_{0}: \mu \leq 85, \quad H_{1}: \mu>85\) c. \(H_{0}: \mu=33, \quad H_{1}: \mu \neq 33\) Show the rejection and nonrejection regions for each of these cases by drawing a sampling distribution curve for the sample mean, assuming that it is normally distributed.

What does the level of significance represent in a test of hypothesis? Explain.

By rejecting the null hypothesis in a test of hypothesis example, are you stating that the alternative hypothesis is true?

For each of the following examples of tests of hypotheses about \(\mu\), show the rejection and nonrejection regions on the sampling distribution of the sample mean assuming that it is normal. a. A two-tailed test with \(\alpha=.05\) and \(n=40\) b. A left-tailed test with \(\alpha=.01\) and \(n=20\) c. A right-tailed test with \(\alpha=.02\) and \(n=55\)

A random sample of 18 observations produced a sample mean of \(9.24\). Find the critical and observed values of \(z\) for each of the following tests of hypothesis using \(\alpha=.05 .\) The population standard deviation is known to be \(5.40\) and the population distribution is normal. a. \(H_{0}: \mu=8.5\) versus \(H_{1}: \mu \neq 8.5\) b. \(H_{0}=\mu=8.5\) versus \(H_{1}: \mu>8.5\)

Consider the null hypothesis \(H_{0}: \mu=5 .\) A random sample of 140 observations is taken from a population with \(\sigma=17\). Using \(\alpha=.05\), show the rejection and nonrejection regions on the sampling distribution curve of the sample mean and find the critical value(s) of \(z\) for the following. \(\begin{array}{lll}\text { a. a right-tailed test } & \text { b. a left-tailed test } & \text { c. a two-tailed test }\end{array}\)